Large-Time Solution of a Nonlinear Diffusion Equation

In this paper we consider the way in which the solution to a class of initial-boundary-value problems for the plane nonlinear diffusion equation partial/partial t= partial} {partial x}(u^βfrac{partial u/partial x), t >=slant 0, x >=slant 0, β > 0, approaches the similarity form as t -> ∞. The problem we solve is chosen for two main reasons: firstly the equation above is of widespread use in modelling physical situations and secondly it provides a tractable but significant example of a free boundary problem.